He wants to have his own way (in which) he can do whatever he likes
主句：He wants to have his own way.
从句：he can do whatever he likes in (which = his own way).从句引导词which指代way,in which在从句中作状语,整个从句是修饰way的定语,所以是定语从句.
He wants to have his own way (that) he can do whatever he likes
主句：He wants to have his own way.
从句：he can do whatever he likes.整个从句和his own way等价,that不指代任何先行词（因为that还原不到从句里面去作任何成分）.所以这是同位语从句.